Can I get my diploma apostilled while I am in Korea? I'm from the UK.

Yes, you can. There are services available in the UK that can take care of the apostille process for you, and they can expedite the process as well. If you search like "UK Apostille service" in google, you will find many.

One of Korvia's recruits used https://www.hagueapostille.co.uk They were fast and reliable. The apostille is £66 and just takes a day or two. The courier shipping is £70, but there are cheaper shipping options available.